Klein, D., Pielaszkiewicz, J., Filipiak, K.Approximate normality in testing an exchangeable covariance structure under large- and high-dimensional settings. Journal of Multivariate Analysis 192, 2022, art.no. 105049, Q2, počet citácií 1

Filipiak, K., Klein, D. Approximation with a Kronecker product structure with one component as compound symmetry or autoregression. Linear Algebra and its Applications 55, 2018, s. 11-33, Q2, citations 2

Filipiak, K., Klein, D., Vojtková, E. The properties of partial trace and block trace operators of partitioned matrices. Electronic Journal of Linear Algebra 33, 2018, s. 3-15, Q3, citations 3

Žežula, I., Klein, D., Roy, A. Testing of multivariate repeated measures data with block exchangeable covariance structure. Test 27(2), 2018, s. 360-378, Q2, citations 4

Jurková, V., Žežula, I., Klein, D. Testing in the growth curve model with intraclass correlation structure. Statistics 54(5), 2020, s. 1124-1146, Q3, citations 1

VEGA 1/0344/14: Mathematical and statistical methods in economic decision making, deputy principal investigator.

Summary: The projekt deals with the mathematical, statistical and computational analysis and prediction of complex economic, social, medical and technical data. The basic research fields are:

1. analysis of multidimensional data with special emphasis on linear models,

3. analysis of extreme values in economic and financial systems,

4. prediction of time series in linear regression models,

2. analysis of behavious of autonomous economic agenst in their effort for optimal solutions and computational complexity of algorithms for these solutions.

VEGA 1/0073/15: Scalable computing methods of structured and unstructured data analysis with uncertainty, grant team member.

Summary: The main aim of the proposed project is to develop new techniques and apply the existing methods for effective processing of structured and unstructured data with uncertainty. The structures of data can be more complex and hardly formalized. Our research team has been investigated these issues on a long-term basis and disposes of several computational methods of data retrieval, analysis and organization. An existing methods are based on various theoretical results from diverse areas as inductive logic programming, statistical methods, applied algebra, database indexing and natural language processing. The unifying idea of these computational methods is an effort to achieve the precise knowledge despite of heterogeneous, incomplete or uncertain character of input data.

VEGA 1/0311/18: Problems of optimal decisions in complex data structures, principal investigator.

Summary: The project deals with methodology of optimal decision-making in models describing complex economic, social, medical and technical phenomena. Its basic research areas are:

1. analysis of models of multivariate data with different dependence structures with special regard to linear models,

2. analysis of behaviour of autonomuous economic agents from viewpoint of their effort for optimal solution and analysis of manipulability of proposed algorithms, computational complexity of these algorithms,

3. analysis of optimal decision in choice of portfolios in economic and financial systems,

4. problems of optimal prediction in regression models of time series.

APVV-17-0568: Applicatons of mathematical methods in economic and medical decision-making, principal investigator.

Summary: Project focuses on development and application of mathematical methods in economic and medical decisionmaking. Partial goals:

1. Application and research of linear modelling methods and optimal empirical predictions in economic and medical data.

2. Analysis of uni- and multivariate medical data with special regard to linear and generalized linear models.

3. Decision-making on optimal allocation in financial portfolios with uncertainty in parameters.

4. Research and comparison of models of search and allocation of kidneys for transplantations, and related models.

5. Development of software for corresponding analyses.

VVGS-2018-895: Probability, statistics and their applications, principal investigator, 2018-2019

Summary: In learning the probability, statistics, and applied courses, an indispensable tools for the taught concepts are graphical and simulation illustrations, since the key term of randomness is harder to understand without visualisation. Current software options allow us to move from classical to modern lessons, and so clearly, comprehensibly and comprehensively demonstrate the important concepts that conceal in themselves. This project focuses on the preparation of such materials (presentations, animations, applets, simulations) in the probability, statistcs and financial mathematics courses.